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A decision tree is a mathematical model used to help managers make decisions. It is a graphical

representation of the alternative course of actions available, their costs, their outcomes and

expected values based on the probability and risks associated with the possible alternatives.

 A decision tree helps to decide whether the net gain from a decision is worthwhile.

Let's look at an example of how a decision tree is constructed. We'll use the following data

A decision tree starts with a decision to be made and the options that can be taken. !here is

always an option to decide to do nothing"

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!he first task is to add possible outcomes to the tree #note circles represent uncertain outcomes$

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 %ext we add in the associated costs, outcome probabilities and financial results for eachoutcome.

!hese probabilities are particularly important to the outcome of a decision tree.

&robability is

• !he percentage chance or possibility that an event will occur 

• anges between ( #())*$ and )

• If all the outcomes of an event are considered, the total probability must add up to (

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+inally we complete the maths in the model by calculating

Expected value:

!he financial value of an outcome calculated by multiplying the estimated  financial effect by itsprobability

Net gain:

!he value to be gained from taking a decision.

 %et gain is calculated by adding together the expected value of each outcome and deducting thecosts associated with the decision.

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Let's look at the calculations. What do they suggest is the best option

Option: Launch loyalty card:

-igh sales #). x /(,))),)))$ 0 /)),)))

Low sales #).1 x /23),)))$ 0 /4)),)))

!otal expected value 0 /5)),)))

Net gain: £900,000 £!00,000 " £#00,000

Option: $ut prices:

-igh sales #).6 x /6)),)))$ 0 /1),)))

Low sales #).7 x /3)),)))$ 0 /()),)))

!otal expected value 0 /21),)))

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Net gain: £%#0,000 £&00,000 " £'#0,000

8oth options indicate a positive net gain, suggesting that either would be better than doing

nothing.

-owever, launching the loyalty card has a higher net gain 9 looks the best option of the twoconsidered

(ENE)*+ O) -*N /E$**ON +EE

:hoices are set out in a logical way

&otential options 9 choices are considered at the same time

;se of probabilities enables the asy to understand 9 tangible results

/12(1$3 O) -*N /E$**ON +EE

&robabilities are ?ust estimates @ always prone to error 

;ses uantitative data only @ ignores ualitative aspects of decisions

Assignment of probabilities and expected values prone to bias

BecisionCmaking techniue doesnDt necessarily reduce the amount of risk